The trigonometry of a tetrahedron explains the relationships between the lengths and various types of angles of a general tetrahedron. The following are...

solid angles and polytopes such as tetrahedrons and n-simplices. In spherical trigonometry, triangles on the surface of a sphere are studied. The spherical...

theorem Trigonometric function Trigonometry of a tetrahedron Triangle (also see List of triangle topics) Sine, Cosine, Tangent (trigonometric function)...

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six...

Charles (ed.). Elements of Geometry and Trigonometry. New York: A. S. Barnes & Co. p. 197. Stillwell, John (1992). Geometry of Surfaces. Universitext....

determine a solid figure called tetrahedron. In non-Euclidean geometries, three "straight" segments (having zero curvature) also determine a "triangle"...

Law of Sines In trigonometry, the law of sines (sometimes called the sine formula or sine rule) is a mathematical equation relating the lengths of the...

theorem Pythagorean triangle Right triangle Triangle inequality Trigonometry List of trigonometry topics Wallpaper group 3D projection 3D computer graphics...

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The...

a special case of the more general law of cosines, valid for arbitrary triangles. In a right triangle with sides a, b and hypotenuse c, trigonometry determines...

Schläfli. As right triangles provide the basis for trigonometry, orthoschemes form the basis of a trigonometry of n dimensions, as developed by Schoute who called...

using trigonometry as below, or the incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular case of acute...

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one...

and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important...

of trigonometry and also solved several problems of spherical trigonometry. He was the first whose quantitative and accurate models for the motion of...

Inequality Of Diagonal". Archived from the original on 2014-10-24. Retrieved 2011-09-26. C. V. Durell & A. Robson, Advanced Trigonometry, Dover, 2003...

the reciprocal square root of 6. The edge lengths of a regular tetrahedron (t), a regular octahedron (o), and a cube (c) of equal total surface areas satisfy...

referenced to the tetrahedron as volumetric unity. The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the...

define sine, cosine, and π in a way that is totally independent of trigonometry, in which case the proof is valid by the change of variables formula and Fubini's...

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...

the volume of a tetrahedron, cylinder, cone, and sphere, for which proofs are given in book XII of Euclid's Elements. In Measurement of a Circle, Archimedes...

height; Tetrahedron – 2 12 a 3 {\textstyle {{\sqrt {2}} \over 12}a^{3}} , where a {\textstyle a} is the side's length. The basic quantities describing a sphere...

any plane containing a bimedian (connector of opposite edges' midpoints) of a tetrahedron bisects the volume of the tetrahedron: pp.89–90  Weisstein,...

equal in length, and their symmetries are C4v of order 8 and C5v of order 10, respectively. A tetrahedron or triangular pyramid is an example that has...

70.5^{\circ }} for the tetrahedron. θ c u b e = π / 2 = 90 ∘ {\displaystyle \theta _{\mathrm {cube} }=\pi /2=90^{\circ }} , a right angle, for the cube...

non-coplanar points A, B, C, and D in 3D form a tetrahedron. In this case, the strict inequality holds: A B ¯ ⋅ C D ¯ + B C ¯ ⋅ D A ¯ > A C ¯ ⋅ B D ¯ {\displaystyle...

with the symmetry groups of regular polyhedra in the three-dimensional Euclidean space: Δ(2,3,3) corresponds to the tetrahedron, Δ(2,3,4) to both the cube...

one same object, acquiring two images from different points of view. In terms of trigonometry relations, depth information can be calculated from disparity...

essentials of arithmetic, geometry, algebra and trigonometry. McGraw-Hill. p. 422. Alexander Zawaira; Gavin Hitchcock (2009). "Lemma 1: In a right-angled...

"Euclidean geometry", Encyclopedia of Mathematics, EMS Press, 2001 [1994] "Plane trigonometry", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Kiran...